Velocity and kinetic energy of a neutron

Calculate the velocity and kinetic energy of a neutron (mass 1.675x10-27kg) that has a wavelength of 0.2nm. How does this compare to the average kinetic energy of a gas molecule at room temperature (0.038eV at 200C)?

1. E=mc^2

2. KE = 1/2 mv^2

I used 1. to calculate the energy which was 1.51 x10^-10 J

Then i subbed the energy into 2. and got a velocity of 4.24 x10^8 m/s

LOL obviously i'm going wrong some where how can a neutron be going faster than light!

First, the expression E=mc^2 does not give the kinetic energy of a particle. Second, even if it did, your method is immune to the given wavelength, so that should give you some idea where you should be looking.